#1 uloha, dvojstranny interval

x=c(5.03,5.06,5.2,5.04,5.02);x

v=t.test(x,conf.level=0.95) #pre overenie
v$conf.int  #pre overenie

g=0.95;g
s = var(x)
m = mean(x)
n = length(x); n
kvt = qt((1+g)/2,n-1); kvt
m_D2=m-kvt*sqrt(s) / sqrt(n); m_D2 #dolne ohr
m_H2=m+kvt*sqrt(s) / sqrt(n); m_H2 #horne


#2 uloha,, t-test, alpha=0.05

x=c(2.5,2.8,2.3,2.2,2.5,2.1,2.2,2.6);x
y=c(2.6,2.8,2.4,2.6,2.7,2.5,2.5);y

#najprv otestujeme var.test...

v1 = var (x); v2=var(y); v1;v2
v1/v2
var.test(x,y,ratio = 1, alternative = "two.sided")
#hodnota p-value je 0.18, co nie je menej ako 0.05, preto nulovu hypotezu nezamietame, tj. predpokladame rovnost s


t.test(x,y,var.equal=T,alternative="greater")

t.test(x,y,var.equal=T,alternative="two.sided")

t.test(x,y,var.equal=T,alternative="less") #p-value je menej ako hladina testu 0.05, pretu nulovu zamietame, plati h1, tj x<y
#tzn., x-y < 0 => x < y, tzn nove hodnoty su lepsie, co mozno pozorovat aj z s^2 :)

#3 uloha

x=c(0.5,1.2,1.3,1.4,1.8,1.9)
y=c(4.297443,7.640234,8.338593,9.110400,13.099295,14.371789)

#spravime dve modeli
plot(x,y)
cor(x,y)
cor.test(x,y)
#z korelacneho testu vidime istu zavislost, ale linearnu ....
#skumame blizsie
testuj <- function(x,y) {

  #hore zmazat
  plot(y~x)
  z1=exp(x)
  v1=lm(y~z1)
  lines(x,v1$fit)
  
  yod1=v1$coef[1] + v1$coef[2]*z1;
  lines(x,yod1, col='red')
  
  lines(x,v1$fit, col='orange')
 
   z2=log(x)
  v2=lm(y~z2)
  summary(v2)
  
  yod2=v2$coef[1] + v2$coef[2]*z2;
  lines(x,yod2, col='blue')
  
  cf <- round(coef(v1), 2)
  cf
  eq1 <- paste0("y = ", cf[1],
               ifelse(sign(cf[2])==1, " + ", " - "), abs(cf[2]), " exp(x)")
 
  
  cf2 <- round(coef(v2), 2)
  eq2 <- paste0("y = ", cf2[1], ifelse(sign(cf2[2])==1, " + ", " - "), abs(cf2[2]), "ln(x)")
 
  
  
  list(Prva = eq1, 'Prva P Hodnota' =   summary(v1)$coefficients[,4],  Druha= eq2, "Druha p hodnota" =   summary(v2)$coefficients[,4])
  
}
dev.off()
testuj(x,y)


#5 uloha: 
x1=c(2.5,2.8,2.3,2.2,2.5,2.1,2.2,2.6);x1
x2=c(2.6,2.8,2.4,2.6,2.7,2.5,2.5);x2
testy <- function(x1,x2,alpha) {
  varEquals = !var.test(x1,x2,ratio = 1, alternative = "two.sided")$p.value < 0.05;
  if(t.test(x1,x2,alternative="two.sided",var.equal=varEquals,conf.level=alpha)$p.value < alpha) "H0 zamietame"
  else "H0 nezamietame"
  t.test(x1,x2,alternative="two.sided",var.equal=varEquals,conf.level=alpha)$p.value
}

testy(x1,x2,0.05)